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A257722
Hexagonal numbers (A000384) that are the sum of eleven consecutive hexagonal numbers.
4
946, 1540, 13695, 1151403, 18773128, 1590903028, 25941294753, 2198372138061, 20904988593016, 35846699817610, 340877159895525, 28887334308843153, 471037447946228878, 39917653136343078778, 650898046192856866503, 55159780922590010984691
OFFSET
1,1
LINKS
Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,25091193602,-25091193602,0,0,0,0,0,0,-1,1).
FORMULA
G.f.: -11*x*(21*x^16 +252*x^15 +4025*x^14 +359100*x^13 +5562025*x^12 +496218492*x^11 +4272895055*x^10 +3412929546*x^9 -457241153867*x^8 +197493713028*x^7 +2213671975*x^6 +142920900*x^5 +1601975*x^4 +103428*x^3 +1105*x^2 +54*x +86) / ((x -1)*(x^2 -20*x +1)*(x^2 +20*x +1)*(x^4 +398*x^2 +1)*(x^8 +158402*x^4 +1)).
EXAMPLE
946 is in the sequence because H(22) = 946 = 1 + 6 + 15 + 28 + 45 + 66 + 91 + 120 + 153 + 190 + 231 = H(1)+...+H(11).
PROG
(PARI) Vec(-11*x*(21*x^16 +252*x^15 +4025*x^14 +359100*x^13 +5562025*x^12 +496218492*x^11 +4272895055*x^10 +3412929546*x^9 -457241153867*x^8 +197493713028*x^7 +2213671975*x^6 +142920900*x^5 +1601975*x^4 +103428*x^3 +1105*x^2 +54*x +86) / ((x -1)*(x^2 -20*x +1)*(x^2 +20*x +1)*(x^4 +398*x^2 +1)*(x^8 +158402*x^4 +1)) + O(x^100))
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Colin Barker, May 06 2015
STATUS
approved