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A102296
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a(n) = (1/6)*(n+1)*(10*n^2 + 17*n + 12).
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1
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2, 13, 43, 102, 200, 347, 553, 828, 1182, 1625, 2167, 2818, 3588, 4487, 5525, 6712, 8058, 9573, 11267, 13150, 15232, 17523, 20033, 22772, 25750, 28977, 32463, 36218, 40252, 44575, 49197, 54128, 59378, 64957, 70875, 77142, 83768, 90763, 98137
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OFFSET
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0,1
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COMMENTS
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A floretion-generated sequence which arises from a particular transform of the centered square numbers: A001844. Specifically, (a(n)) is the jesfor-transform of the sequence A001844 with respect to the floretion given in the program code. The sequence relates centered square numbers, triangular numbers and centered octahedral numbers to (n+1)^3. Note: this was made possible in part by the formula already given for A085786.
Floretion Algebra Multiplication Program, FAMP Code: 4jesforseq[ + .25'j + .25'k + .25j' + .25k' + .25'ij' + .25'ik' + .25'ji' + .25'ki' + e ], vesforseq = A001844, ForType: 1A, LoopType: tes.
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LINKS
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FORMULA
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G.f.: (x+1)*(3x+2)/(x-1)^4;
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MATHEMATICA
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LinearRecurrence[{4, -6, 4, -1}, {2, 13, 43, 102}, 50] (* Paolo Xausa, Mar 09 2024 *)
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PROG
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(Magma) [(1/6)*(n+1)*(10*n^2+17*n+12): n in [0..50]]; // Vincenzo Librandi, May 30 2011
(PARI) a(n) = (n+1)*(10*n^2+17*n+12)/6
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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