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A218326 Odd octagonal pyramidal numbers 1
1, 9, 135, 231, 765, 1045, 2275, 2835, 5049, 5985, 9471, 10879, 15925, 17901, 24795, 27435, 36465, 39865, 51319, 55575, 69741, 74949, 92115, 98371, 118825, 126225, 150255, 158895, 186789, 196765, 228811, 240219, 276705, 289641, 330855, 345415, 391645, 407925 (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) + 384.
a(n) = (4*n-(-1)^n-1)*(4*n-(-1)^n-3)*(4*n-(-1)^n-4)/8.
G. f. x(1+8*x+123*x^2+72*x^3+159*x^4+16*x^5+5*x^6)/((1-x)^4*(1+x)^3).
EXAMPLE
The sequence of octagonal pyramidal numbers A002414 begins 1, 9, 30, 70, 135, 231, 364, 540, 765, 1045, … As the third odd term is 135, then a(3) = 135.
MATHEMATICA
LinearRecurrence[{1, 3, -3, -3, 3, 1, -1}, {1, 9, 135, 231, 765, 1045, 2275}, 38]
CROSSREFS
Sequence in context: A296171 A167893 A268062 * A272498 A254282 A235339
KEYWORD
nonn
AUTHOR
Ant King, Oct 27 2012
STATUS
approved

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Last modified April 18 03:01 EDT 2024. Contains 371767 sequences. (Running on oeis4.)