A369836
Number of compositions of 5*n into parts 1 and 5.
Original entry on oeis.org
1, 2, 8, 34, 140, 571, 2328, 9496, 38740, 158045, 644761, 2630364, 10730820, 43777405, 178594110, 728591751, 2972359720, 12126025705, 49469281395, 201814663875, 823322219501, 3358821723401, 13702634402876, 55901207340276, 228054320813276, 930369409108152
Offset: 0
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LinearRecurrence[{6, -10, 10, -5, 1}, {1, 2, 8, 34, 140}, 50] (* Paolo Xausa, Mar 15 2024 *)
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a(n) = sum(k=0, n, binomial(n+4*k, n-k));
A373928
Number of compositions of 7*n-2 into parts 1 and 7.
Original entry on oeis.org
1, 7, 35, 168, 819, 4025, 19796, 97315, 478304, 2350860, 11554621, 56791883, 279136551, 1371977475, 6743373646, 33144194898, 162906243014, 800696596250, 3935484773527, 19343207491818, 95073338508548, 467292702057555, 2296779231936167, 11288844908179562
Offset: 1
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a[n_]:= n*(1 + n)*(2 + n)*(3 + n)*(4 + n)*HypergeometricPFQ[{1-n, (5+n)/6, 1+n/6, (7+n)/6, (8+n)/6, (9+n)/6, (10+n)/6}, {6/7, 8/7, 9/7, 10/7, 11/7, 12/7}, -6^6/7^7]/120; Array[a,24] (* Stefano Spezia, Jun 23 2024 *)
LinearRecurrence[{8,-21,35,-35,21,-7,1},{1,7,35,168,819,4025,19796},40] (* Harvey P. Dale, Jul 28 2024 *)
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a(n) = sum(k=0, n, binomial(n+4+6*k, n-1-k));
A369838
Number of compositions of 5*n-3 into parts 1 and 5.
Original entry on oeis.org
1, 4, 15, 60, 245, 1001, 4085, 16665, 67985, 277350, 1131476, 4615966, 18831276, 76823991, 313410816, 1278589392, 5216127688, 21279691689, 86812537085, 354160046356, 1444829775128, 5894321227301, 24046447082350, 98099780277675, 400207434286276, 1632684497403029
Offset: 1
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LinearRecurrence[{6, -10, 10, -5, 1}, {1, 4, 15, 60, 245}, 50] (* Paolo Xausa, Mar 15 2024 *)
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a(n) = sum(k=0, n, binomial(n+1+4*k, n-1-k));
A369839
Number of compositions of 5*n-4 into parts 1 and 5.
Original entry on oeis.org
1, 3, 11, 45, 185, 756, 3084, 12580, 51320, 209365, 854126, 3484490, 14215310, 57992715, 236586825, 965178576, 3937538296, 16063564001, 65532845396, 267347509271, 1090669728772, 4449491452173, 18152125855049, 74053333195325, 302107654008601, 1232477063116753
Offset: 1
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LinearRecurrence[{6, -10, 10, -5, 1}, {1, 3, 11, 45, 185}, 50] (* Paolo Xausa, Mar 15 2024 *)
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a(n) = sum(k=0, n, binomial(n+4*k, n-1-k));
Showing 1-4 of 4 results.