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Search: id:A080851
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| A080851 |
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Square array of pyramidal numbers, read by antidiagonals. |
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+0
2
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| 1, 1, 3, 1, 4, 6, 1, 5, 10, 10, 1, 6, 14, 20, 15, 1, 7, 18, 30, 35, 21, 1, 8, 22, 40, 55, 56, 28, 1, 9, 26, 50, 75, 91, 84, 36, 1, 10, 30, 60, 95, 126, 140, 120, 45, 1, 11, 34, 70, 115, 161, 196, 204, 165, 55, 1, 12, 38, 80, 135, 196, 252, 288, 285, 220, 66, 1, 13, 42, 90, 155
(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+2, 2)+n*C(k+2, 3). T(n, k)=T(n-1, k)+C(k+2, 3) = T(n-1, k)+k(k+1)(k+2)/6 G.f. for rows : (1+nx)/(1-x)^4, n>=-1
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EXAMPLE
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Array (n>=0,k>=0) begins
1 3 6 10 15 21 28 ...
1 4 10 20 35 56 84 ...
1 5 14 30 55 91 140 ...
1 6 18 40 75 126 196 ...
1 7 22 50 95 161 252 ...
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PROGRAM
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(Derive). vector(vector(poly_coeff(Taylor((1+kx)/(1-x)^4, x, 11), x, n), n, 0, 11), k, -1, 10) VECTOR(VECTOR(comb(k+2, 2)+comb(k+2, 3)n, k, 0, 11), n, 0, 11)
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CROSSREFS
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Numerous sequences in the database are to be found in the array. Rows include the pyramidal numbers A000217, A000292, A000330, A002411, A002412, A002413, A002414, A007584, A007585, A007586.
Columns include or are closely related to A017029, A017113, A017017, A017101, A016777, A017305. Diagonals include A006325, A006484, A002417.
Cf. A057145.
Sequence in context: A116416 A051203 A086271 this_sequence A108285 A075419 A060922
Adjacent sequences: A080848 A080849 A080850 this_sequence A080852 A080853 A080854
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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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