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A134658
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Triangle read by rows, giving coefficients of extended Jacobsthal recurrence.
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3
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3, 1, 2, 2, -1, 2, 3, -3, 1, 2, 4, -6, 4, -1, 2, 5, -10, 10, -5, 1, 2, 6, -15, 20, -15, 6, -1, 2, 7, -21, 35, -35, 21, -7, 1, 2, 8, -28, 56, -70, 56, -28, 8, -1, 2, 9, -36, 84, -126, 126, -84, 36, -9, 1, 2, 10, -45, 120, -210, 252, -210, 120, -45, 10, -1, 2
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OFFSET
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0,1
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COMMENTS
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Sequence identical to half its p-th differences from the second term.
This sequence is the second of a family after A135356.
This triangle looks like a Pascal's triangle without first column, and with signs and with additional right diagonal consisting of 2's. - Michel Marcus, Apr 07 2019
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LINKS
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FORMULA
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EXAMPLE
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Triangle begins
3; : A000244 = 1, 3, 9, 27, ... is the main sequence
1, 2; : A001045 = 0, 1, 1, 3, ... is the main sequence
2, -1, 2; : 0, 0, (A007910 = 1, 2, 3, ... ) is the main sequence
3, -3, 1, 2; : 0, 0, 0, 1, 3, 6, 10, 17, ... is the main sequence
4, -6, 4, -1, 2; : A134987 = 0, 0, 0, 0, 1, ... is the main sequence
...
See signatures of linear recurrence of corresponding sequences.
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MATHEMATICA
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T[n_, k_] := T[n, k] = Which[n == 0, 3, k == n, 2, k == 0, n, k == n-1, (-1)^k, True, T[n-1, k] - T[n-1, k-1]];
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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In agreement with author, T(0, 0) = 3 and offset 0 by Michel Marcus, Apr 06 2019
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STATUS
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approved
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