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Search: id:A080852
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| A080852 |
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Square array of 4D pyramidal numbers, read by antidiagonals. |
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+0
1
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| 1, 1, 4, 1, 5, 10, 1, 6, 15, 20, 1, 7, 20, 35, 35, 1, 8, 25, 50, 70, 56, 1, 9, 30, 65, 105, 126, 84, 1, 10, 35, 80, 140, 196, 210, 120, 1, 11, 40, 95, 175, 266, 336, 330, 165, 1, 12, 45, 110, 210, 336, 462, 540, 495, 220, 1, 13, 50, 125, 245, 406, 588, 750, 825, 715, 286, 1
(list; table; graph; listen)
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OFFSET
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0,3
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FORMULA
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T(n, k)=C(k+3, 3)+n*C(k+3, 4) T(n, k)=T(n-1, k)+C(k+3, 4)=T(n-1, k)+k(k+1)(k+2)(k+3)/24 G.f. for rows : (1+nx)/(1-x)^5, n>=-1
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EXAMPLE
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Array (n>=0, k>=0) begins
1 4 10 20 35 56 ...
1 5 15 35 70 126...
1 6 20 50 105 196...
1 7 25 65 140 266...
1 8 30 80 175 336...
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PROGRAM
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(Derive) vector(vector(poly_coeff(Taylor((1+kx)/(1-x)^5, x, 11), x, n), n, 0, 11), k, -1, 10) VECTOR(VECTOR(comb(k+3, 3)+comb(k+3, 4)n, k, 0, 11), n, 0, 11)
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CROSSREFS
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Rows include A000292, A000332, A002415, A001296, A002418, A002419, A051740, A051797
Cf. A057145, A080851.
Sequence in context: A016687 A139356 A155060 this_sequence A090842 A120868 A100279
Adjacent sequences: A080849 A080850 A080851 this_sequence A080853 A080854 A080855
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KEYWORD
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easy,nonn,tabl
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), Feb 21 2003
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