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A276042 Exponential convolution of central polygonal numbers (A000124) with themselves. 0
1, 4, 16, 62, 230, 812, 2728, 8752, 26944, 80000, 230144, 644096, 1759744, 4707328, 12359680, 31920128, 81231872, 204013568, 506331136, 1243217920, 3022913536, 7285243904, 17415274496, 41321234432, 97370767360, 227993976832, 530713673728 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..26.

M. Bernstein and N. J. A. Sloane, Some canonical sequences of integers, Linear Alg. Applications, 226-228 (1995), 57-72. Erratum 320 (2000), 210. [Link to arXiv version]

M. Bernstein and N. J. A. Sloane, Some canonical sequences of integers, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to Lin. Alg. Applic. version together with omitted figures]

Index entries for sequences related to centered polygonal numbers

Index entries for linear recurrences with constant coefficients, signature (10,-40,80,-80,32)

FORMULA

O.g.f.: (1 - 6*x + 16*x^2 - 18*x^3 + 10*x^4)/(1 - 2*x)^5.

E.g.f.: (2 + 2*x + x^2)^2*exp(2*x)/4.

a(n) = 10*a(n-1) - 40*a(n-2) + 80*a(n-3) - 80*a(n-4) + 32*a(n-5).

a(n) = 2^(n - 6)*(n^4 + 2*n^3 + 19*n^2 + 42*n + 64).

MATHEMATICA

LinearRecurrence[{10, -40, 80, -80, 32}, {1, 4, 16, 62, 230}, 27]

Table[2^(n - 6) (n^4 + 2 n^3 + 19 n^2 + 42 n + 64), {n, 0, 26}]

CROSSREFS

Cf. A000124, A007465.

Sequence in context: A283858 A283409 A192468 * A084859 A081666 A250346

Adjacent sequences:  A276039 A276040 A276041 * A276043 A276044 A276045

KEYWORD

nonn,easy

AUTHOR

Ilya Gutkovskiy, Aug 27 2016

STATUS

approved

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Last modified May 24 18:34 EDT 2019. Contains 323534 sequences. (Running on oeis4.)