A051868 -id:A051868

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A360436

32-gonal numbers: a(n) = n*(15*n-14).

+0
1

0, 1, 32, 93, 184, 305, 456, 637, 848, 1089, 1360, 1661, 1992, 2353, 2744, 3165, 3616, 4097, 4608, 5149, 5720, 6321, 6952, 7613, 8304, 9025, 9776, 10557, 11368, 12209, 13080, 13981, 14912, 15873, 16864, 17885, 18936, 20017, 21128, 22269, 23440, 24641, 25872

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,3

LINKS

Table of n, a(n) for n=0..42.

Index to sequences related to polygonal numbers

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

FORMULA

G.f.: x*(1 + 29*x)/(1 - x)^3.

E.g.f.: exp(x)*(x + 15*x^2).

MATHEMATICA

Table[n (15 n - 14), {n, 30}]

PROG

(PARI) a(n)=n*(15*n-14) \\ Charles R Greathouse IV, Feb 07 2023

CROSSREFS

Cf. A051868, A254474, A161935, A282853.

KEYWORD

nonn,easy

AUTHOR

Nikolaos Pantelidis, Feb 07 2023

STATUS

approved

A373665

Positive integers that cannot be written as a sum of a practical number and a 16-gonal number.

+0
1

10, 11, 14, 15, 23, 26, 27, 35, 38, 39, 45, 50, 59, 62, 68, 71, 74, 83, 86, 95, 98, 102, 103, 107, 110, 114, 115, 119, 122, 131, 134, 137, 138, 139, 143, 155, 158, 159, 164, 167, 170, 174, 179, 182, 183, 186, 190, 191, 194, 202, 203, 206, 215, 219, 227, 230

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

Somu and Tran (2024) proved that there are infinitely many such integers. More generally, infinitely many positive integers cannot be written as a sum of a practical number and an s-gonal number if s is congruent to 4 modulo 12.

LINKS

Duc Van Khanh Tran, Table of n, a(n) for n = 1..10000

Sai Teja Somu and Duc Van Khanh Tran, On sums of practical numbers and polygonal numbers, Journal of Integer Sequences, 27(5), 2024.

CROSSREFS

Cf. A005153, A051868.

KEYWORD

nonn

AUTHOR

Duc Van Khanh Tran, Jun 12 2024

STATUS

approved

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