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A294276
Sum of the ninth powers of the parts in the partitions of n into two parts.
1
0, 2, 513, 20708, 282340, 2255148, 12313161, 52928912, 186884496, 576258110, 1574304985, 3942330372, 9092033028, 19736886008, 40357579185, 78935156288, 147520415296, 266495712282, 464467582161, 788155279940, 1299155279940, 2095793274212, 3300704544313
OFFSET
1,2
LINKS
Index entries for linear recurrences with constant coefficients, signature (1,10,-10,-45,45,120,-120,-210,210,252,-252,-210,210,120,-120,-45,45,10,-10,-1,1).
FORMULA
a(n) = Sum_{i=1..floor(n/2)} i^9 + (n-i)^9.
From Colin Barker, Nov 21 2017: (Start)
G.f.: x^2*(2 + 511*x + 20175*x^2 + 256522*x^3 + 1770948*x^4 + 7464688*x^5 + 21796206*x^6 + 45087574*x^7 + 69569484*x^8 + 79813090*x^9 + 69501528*x^10 + 45087574*x^11 + 21722580*x^12 + 7464688*x^13 + 1756842*x^14 + 256522*x^15 + 19674*x^16 + 511*x^17+ x^18) / ((1 - x)^11*(1 + x)^10).
a(n) = a(n-1) + 10*a(n-2) - 10*a(n-3) - 45*a(n-4) + 45*a(n-5) + 120*a(n-6) - 120*a(n-7) - 210*a(n-8) + 210*a(n-9) + 252*a(n-10) - 252*a(n-11) - 210*a(n-12) + 210*a(n-13) + 120*a(n-14) - 120*a(n-15) - 45*a(n-16) + 45*a(n-17) + 10*a(n-18) - 10*a(n-19) - a(n-20) + a(n-21) for n>21.
(End)
MATHEMATICA
Table[Sum[i^9 + (n - i)^9, {i, Floor[n/2]}], {n, 40}]
PROG
(PARI) concat(0, Vec(x^2*(2 + 511*x + 20175*x^2 + 256522*x^3 + 1770948*x^4 + 7464688*x^5 + 21796206*x^6 + 45087574*x^7 + 69569484*x^8 + 79813090*x^9 + 69501528*x^10 + 45087574*x^11 + 21722580*x^12 + 7464688*x^13 + 1756842*x^14 + 256522*x^15 + 19674*x^16 + 511*x^17+ x^18) / ((1 - x)^11*(1 + x)^10) + O(x^40))) \\ Colin Barker, Nov 21 2017
CROSSREFS
Sequence in context: A234606 A139302 A003391 * A320520 A196290 A182446
KEYWORD
nonn,easy
AUTHOR
Wesley Ivan Hurt, Oct 26 2017
STATUS
approved