A218330 Odd decagonal pyramidal numbers.

1, 11, 175, 301, 1005, 1375, 3003, 3745, 6681, 7923, 12551, 14421, 21125, 23751, 32915, 36425, 48433, 52955, 68191, 73853, 92701, 99631, 122475, 130801, 158025, 167875, 199863, 211365, 248501, 261783, 304451, 319641, 368225, 385451, 440335, 459725, 521293

Offset

1,2

Links

Table of n, a(n) for n=1..37.

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-17)*(4*n-(-1)^n-3)*(4*n-(-1)^n-1)/24.

G. f. x*(1+10*x+161*x^2+96*x^3+215*x^4+22*x^5+7*x^6)/((1-x)^4*(1+x)^3).

Example

The sequence of decagonal pyramidal numbers A007585 begins 0, 1, 11, 38, 90, 175, 301, 476, 708, 1005, 1375,... As the third odd term is 175, then a(3) = 175.

Mathematica

LinearRecurrence[{1, 3, -3, -3, 3, 1, -1}, {1, 11, 175, 301, 1005, 1375, 3003}, 37]

Crossrefs

Cf. A007585, A218331.

Sequence in context: A161355 A223067 A280442 * A365034 A196664 A003729

Adjacent sequences: A218327 A218328 A218329 * A218331 A218332 A218333

Keyword

nonn

Author

Ant King, Oct 29 2012

Status

approved