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A318624 Number of 3-member subsets of [3*n] whose elements sum to a multiple of n. 2
0, 1, 10, 30, 55, 91, 138, 190, 253, 327, 406, 496, 597, 703, 820, 948, 1081, 1225, 1380, 1540, 1711, 1893, 2080, 2278, 2487, 2701, 2926, 3162, 3403, 3655, 3918, 4186, 4465, 4755, 5050, 5356, 5673, 5995, 6328, 6672, 7021, 7381, 7752, 8128, 8515, 8913, 9316 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
FORMULA
G.f.: -x*(3*x^4+4*x^3+11*x^2+8*x+1)/((x^2+x+1)*(x-1)^3).
a(n) = 2*a(n-1) -a(n-2) +a(n-3) -2*a(n-4) +a(n-5) for n>5.
3*a(n) = 5+2*A099837(n)+27*n*(n-1)/2 for n>0. - R. J. Mathar, Sep 02 2018
EXAMPLE
a(1) = 1: {1,2,3}.
a(2) = 10: {1,2,3}, {1,2,5}, {1,3,4}, {1,3,6}, {1,4,5}, {1,5,6}, {2,3,5}, {2,4,6}, {3,4,5}, {3,5,6}.
a(3) = 30: {1,2,3}, {1,2,6}, {1,2,9}, {1,3,5}, {1,3,8}, {1,4,7}, {1,5,6}, {1,5,9}, {1,6,8}, {1,8,9}, {2,3,4}, {2,3,7}, {2,4,6}, {2,4,9}, {2,5,8}, {2,6,7}, {2,7,9}, {3,4,5}, {3,4,8}, {3,5,7}, {3,6,9}, {3,7,8}, {4,5,6}, {4,5,9}, {4,6,8}, {4,8,9}, {5,6,7}, {5,7,9}, {6,7,8}, {7,8,9}.
MATHEMATICA
LinearRecurrence[{2, -1, 1, -2, 1}, {0, 1, 10, 30, 55, 91}, 50] (* Harvey P. Dale, Mar 27 2019 *)
CROSSREFS
Row n=3 of A318557.
Sequence in context: A096844 A031299 A124164 * A255601 A104044 A124080
KEYWORD
nonn,easy
AUTHOR
Alois P. Heinz, Aug 30 2018
STATUS
approved

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Last modified July 24 02:45 EDT 2024. Contains 374575 sequences. (Running on oeis4.)