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A199771
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Row sums of the triangle in A199332.
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9
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1, 5, 12, 26, 45, 75, 112, 164, 225, 305, 396, 510, 637, 791, 960, 1160, 1377, 1629, 1900, 2210, 2541, 2915, 3312, 3756, 4225, 4745, 5292, 5894, 6525, 7215, 7936, 8720, 9537, 10421, 11340, 12330, 13357, 14459, 15600, 16820, 18081, 19425, 20812, 22286, 23805
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OFFSET
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1,2
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COMMENTS
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a(n) = sum(A199332(n,k): 1 <= k <= n);
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LINKS
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FORMULA
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G.f. x*( 1+3*x+x^2+x^3 ) / ((1+x)^2*(x-1)^4). - R. J. Mathar, Nov 24 2011
a(n) = n*(3+2*n^2+4*n+(-1)^n))/8. - _R. J. Mathar_, Jun 23 2023
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MATHEMATICA
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LinearRecurrence[{2, 1, -4, 1, 2, -1}, {1, 5, 12, 26, 45, 75}, 50] (* _Harvey P. Dale_, Apr 27 2019 *)
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PROG
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(Haskell)
a199771 = sum . a199332_row
(PARI) a(n)=([0, 1, 0, 0, 0, 0; 0, 0, 1, 0, 0, 0; 0, 0, 0, 1, 0, 0; 0, 0, 0, 0, 1, 0; 0, 0, 0, 0, 0, 1; -1, 2, 1, -4, 1, 2]^(n-1)*[1; 5; 12; 26; 45; 75])[1, 1] \\ _Charles R Greathouse IV_, Jun 18 2017
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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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_Reinhard Zumkeller_, Nov 23 2011
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STATUS
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approved
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