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A218327 Even octagonal pyramidal numbers (A002414) 1
30, 70, 364, 540, 1386, 1794, 3480, 4216, 7030, 8190, 12420, 14100, 20034, 22330, 30256, 33264, 43470, 47286, 60060, 64780, 80410, 86130, 104904, 111720, 133926, 141934, 167860, 177156, 207090, 217770, 252000, 264160, 302974, 316710, 360396, 375804, 424650 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
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)/8
G. f. 2*x(15+20*x+102*x^2+28*x^3+27*x^4)/((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 even term is 364, then a(3) = 364.
MATHEMATICA
LinearRecurrence[{1, 3, -3, -3, 3, 1, -1}, {30, 70, 364, 540, 1386, 1794, 3480}, 37]
CROSSREFS
Sequence in context: A071141 A071312 A071142 * A259753 A308137 A179321
KEYWORD
nonn
AUTHOR
Ant King, Oct 27 2012
STATUS
approved

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Last modified April 14 03:49 EDT 2024. Contains 371655 sequences. (Running on oeis4.)