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A253447
Indices of centered octagonal numbers (A016754) which are also centered heptagonal numbers (A069099).
3
1, 15, 435, 13021, 390181, 11692395, 350381655, 10499757241, 314642335561, 9428770309575, 282548466951675, 8467025238240661, 253728208680268141, 7603379235169803555, 227847648846413838495, 6827826086157245351281, 204606934935870946699921
OFFSET
1,2
COMMENTS
Also positive integers y in the solutions to 7*x^2 - 8*y^2 - 7*x + 8*y = 0, the corresponding values of x being A253446.
LINKS
FORMULA
a(n) = 31*a(n-1)-31*a(n-2)+a(n-3).
G.f.: -x*(x^2-16*x+1) / ((x-1)*(x^2-30*x+1)).
a(n) = (8+(4+sqrt(14))*(15+4*sqrt(14))^(-n)-(-4+sqrt(14))*(15+4*sqrt(14))^n)/16. - Colin Barker, Mar 03 2016
EXAMPLE
15 is in the sequence because the 15th centered octagonal number is 841, which is also the 16th centered heptagonal number.
PROG
(PARI) Vec(-x*(x^2-16*x+1)/((x-1)*(x^2-30*x+1)) + O(x^100))
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Colin Barker, Jan 01 2015
STATUS
approved