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A294273 Sum of the sixth powers of the parts in the partitions of n into two parts. 1
0, 2, 65, 858, 4890, 21244, 67171, 188916, 446964, 994030, 1978405, 3796622, 6735950, 11680408, 19092295, 30745064, 47260136, 71929146, 105409929, 153455810, 216455810, 303993492, 415601835, 566623708, 754740700, 1003708134, 1307797101, 1702747126 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
Index entries for linear recurrences with constant coefficients, signature (1,7,-7,-21,21,35,-35,-35,35,21,-21,-7,7,1,-1).
FORMULA
a(n) = Sum_{i=1..floor(n/2)} i^6 + (n-i)^6.
From Colin Barker, Nov 20 2017: (Start)
G.f.: x^2*(2 + 63*x + 779*x^2 + 3591*x^3 + 10845*x^4 + 19026*x^5 + 23850*x^6 + 19026*x^7 + 10600*x^8 + 3591*x^9 + 723*x^10 + 63*x^11 + x^12) / ((1 - x)^8*(1 + x)^7).
a(n) = (n/42 - n^3/6 + n^5/2 + 1/128*(-63 + (-1)^n)*n^6 + n^7/7).
a(n) = a(n-1) + 7*a(n-2) - 7*a(n-3) - 21*a(n-4) + 21*a(n-5) + 35*a(n-6) - 35*a(n-7) - 35*a(n-8) + 35*a(n-9) + 21*a(n-10) - 21*a(n-11) - 7*a(n-12) + 7*a(n-13) + a(n-14) - a(n-15) for n>15.
(End)
MATHEMATICA
Table[Sum[i^6 + (n - i)^6, {i, Floor[n/2]}], {n, 50}]
PROG
(PARI) concat(0, Vec(x^2*(2 + 63*x + 779*x^2 + 3591*x^3 + 10845*x^4 + 19026*x^5 + 23850*x^6 + 19026*x^7 + 10600*x^8 + 3591*x^9 + 723*x^10 + 63*x^11 + x^12) / ((1 - x)^8*(1 + x)^7) + O(x^40))) \\ Colin Barker, Nov 20 2017
CROSSREFS
Sequence in context: A342608 A294179 A002604 * A199145 A198665 A185029
KEYWORD
nonn,easy
AUTHOR
Wesley Ivan Hurt, Oct 26 2017
STATUS
approved

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Last modified May 18 21:39 EDT 2024. Contains 372666 sequences. (Running on oeis4.)