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A218331 Even, nonzero decagonal pyramidal numbers. 1
38, 90, 476, 708, 1826, 2366, 4600, 5576, 9310, 10850, 16468, 18700, 26586, 29638, 40176, 44176, 57750, 62826, 79820, 86100, 106898, 114510, 139496, 148568, 178126, 188786, 223300, 235676, 275530, 289750, 335328, 351520, 403206, 421498, 479676, 500196 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..36.

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

FORMULA

a(n) = a(n-1) + 3*a(n-2) - 3*a(n-3) - 3*a(n-4) + 3*a(n-5) + a(n-6) - a(n-7).

a(n) = 3*a(n-2) - 3*a(n-4) + a(n-6) + 512.

a(n) = (16*n-4*(-1)^n-1)*(4*n-(-1)^n+3)*(4*n-(-1)^n+1)/24.

G. f. 2*x*(19+26*x+136*x^2+38*x^3+37*x^4)/((1-x)^4*(1+x)^3).

EXAMPLE

The sequence of nonzero decagonal pyramidal numbers begins 1, 11, 38, 90, 175, 301, 476, 708, 1005, 1375,... As the third even term is 476, then a(3) = 476.

MATHEMATICA

LinearRecurrence[{1, 3, -3, -3, 3, 1, -1}, {38, 90, 476, 708, 1826, 2366, 4600}, 36]

CROSSREFS

Cf. A007585, A218330.

Sequence in context: A137028 A235087 A235080 * A124141 A093649 A020167

Adjacent sequences:  A218328 A218329 A218330 * A218332 A218333 A218334

KEYWORD

nonn,easy

AUTHOR

Ant King, Oct 29 2012

STATUS

approved

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Last modified July 13 17:54 EDT 2020. Contains 335689 sequences. (Running on oeis4.)