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A218330 Odd decagonal pyramidal numbers. 1
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 (list; graph; refs; listen; history; text; internal format)
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 * A196664 A003729 A230388

Adjacent sequences:  A218327 A218328 A218329 * A218331 A218332 A218333

KEYWORD

nonn

AUTHOR

Ant King, Oct 29 2012

STATUS

approved

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Last modified February 22 23:03 EST 2019. Contains 320411 sequences. (Running on oeis4.)