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A177747
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Convolution of A008805 (triangular numbers repeated) with itself.
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2
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1, 2, 7, 12, 27, 42, 77, 112, 182, 252, 378, 504, 714, 924, 1254, 1584, 2079, 2574, 3289, 4004, 5005, 6006, 7371, 8736, 10556, 12376, 14756, 17136, 20196, 23256, 27132, 31008, 35853, 40698, 46683, 52668, 59983, 67298, 76153, 85008, 95634, 106260, 118910, 131560, 146510
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OFFSET
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0,2
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (2,3,-8,-2,12,-2,-8,3,2,-1).
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FORMULA
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Square (1 + x + 3x^2 + 3x^3 + 6x^4 + 6x^5 + ...)
a(n) = (n+5)*(2*n*(n+10)*(n^2+10*n+35)+5*(2*n*(n+10)+39)*(-1)^n+573)/3840. [Bruno Berselli, Mar 23 2012]
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EXAMPLE
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As a multiplication table array:
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1, 1, 3, 3, 6,...
1, 1, 3, 3,......
3, 3, 9,.........
3, 3,............
6,...............
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Then taking antidiagonal sums of terms, we obtain 1, (1 + 1) = 2, (3 + 1 + 3) = 7, (3 + 3 + 3 + 3) = 12, (6, + 3 + 9 + 3 + 6) = 27, etc.
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MATHEMATICA
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lst = CoefficientList[ Series[1/((1 - x) (1 - x^2)^2), {x, 0, 111}], x]; t[n_, k_] := lst[[n]] lst[[k]]; f[n_] := Sum[ t[n - m + 1, m], {m, n}]; Array[f, 45] (* Robert G. Wilson v, Dec 18 2010 *)
LinearRecurrence[{2, 3, -8, -2, 12, -2, -8, 3, 2, -1}, {1, 2, 7, 12, 27, 42, 77, 112, 182, 252}, 45] (* Bruno Berselli, Mar 23 2012 *)
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PROG
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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