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A048914
Indices of pentagonal numbers which are also 9-gonal.
3
1, 21, 10981, 252081, 132846121, 3049673901, 1607172358861, 36894954600201, 19443571064652241, 446355157703555781, 235228321132990450741, 5400004661002663236321, 2845792209623347408410361, 65329255942455062129453661, 34428393916794935813958094621, 790353332991816680639467152441
OFFSET
1,2
REFERENCES
Elena Deza and Michel Marie Deza, Figurate numbers, World Scientific Publishing (2012), page 43.
LINKS
Eric Weisstein's World of Mathematics, Nonagonal Pentagonal Number.
FORMULA
From Ant King, Dec 20 2011: (Start)
a(n) = 12098*a(n-2)-a(n-4)-2016.
a(n) = a(n-1)+12098*a(n-2)-12098*a(n-3)-a(n-4)+a(n-5).
a(n) = 1/84*((2+sqrt(21))*(7-sqrt(21)*(-1)^n)*(2*sqrt(7)+3*sqrt(3))^(2n-2)+ (2-sqrt(21))*(7+sqrt(21)*(-1)^n)*(2*sqrt(7)-3*sqrt(3))^(2n-2)+14).
a(n) = ceiling((1/84)*(2+sqrt(21))*(7-sqrt(21)*(-1)^n)*(2*sqrt(7)+3*sqrt(3))^(2n-2)).
G.f.: x*(1+20*x-1138*x^2-860*x^3-39*x^4) / ((1-x)*(1-110*x+x^2)*(1+110*x+x^2)).
Limit_{n->oo} a(2*n+1)/a(2*n) = (527 + 115*sqrt(21))/2.
Limit_{n->oo} a(2*n)/a(2*n-1) = (23 + 5*sqrt(21))/2. (End)
MATHEMATICA
LinearRecurrence[{1, 12098, -12098, -1, 1}, {1, 21, 10981, 252081, 132846121}, 13] (* Ant King, Dec 20 2011 *)
PROG
(PARI) Vec(x*(39*x^4+860*x^3+1138*x^2-20*x-1)/((x-1)*(x^2-110*x+1)*(x^2+110*x+1)) + O(x^20)) \\ Colin Barker, Jun 22 2015
CROSSREFS
Sequence in context: A135823 A013726 A159358 * A046183 A203674 A250065
KEYWORD
nonn,easy
STATUS
approved