A218331 Even, nonzero decagonal pyramidal numbers.

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

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