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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
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
Sequence in context: A161355 A223067 A280442 * A365034 A196664 A003729
KEYWORD
nonn
AUTHOR
Ant King, Oct 29 2012
STATUS
approved

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Last modified April 18 06:24 EDT 2024. Contains 371769 sequences. (Running on oeis4.)