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Search: id:A092422
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| A092422 |
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Triangle, read by rows, where T(n,k) equals the k-th term of the convolution of the (n-k)-th row with the (2k)-th Fibonacci polynomial (A011973). |
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3
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| 1, 1, 1, 1, 2, 1, 1, 3, 4, 1, 1, 4, 8, 7, 1, 1, 5, 14, 18, 11, 1, 1, 6, 21, 40, 36, 16, 1, 1, 7, 30, 72, 98, 66, 22, 1, 1, 8, 40, 119, 211, 214, 113, 29, 1, 1, 9, 52, 182, 398, 546, 428, 183, 37, 1, 1, 10, 65, 265, 692, 1170, 1278, 799, 283, 46, 1, 1, 11, 80, 368, 1123, 2286, 3104
(list; table; graph; listen)
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OFFSET
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0,5
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FORMULA
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T(n, k) = sum_{j=0, min(k, n-k)} binomial(k+j, k-j)*T(n-k, j) with T(n, 0)=1.
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EXAMPLE
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Even-numbered Fibonacci polynomials (cf. A011973) are:
{1},
{1,1},
{1,3,1},
{1,5,6,1},
{1,7,15,10,1},...
These terms are used to generate each row from the prior rows. For example,
row 5 = {1(1), 1(1)+1(4), 1(1)+3(3)+1(4), 1(1)+6(2)+5(1), 1(1)+10(1), 1(1)};
row 6 = {1(1), 1(1)+1(5), 1(1)+3(4)+1(8), 1(1)+6(3)+5(4)+1(1), 1(1)+10(2)+15(1), 1(1)+15(1), 1(1)}.
Rows begin:
{1},
{1,1},
{1,2,1},
{1,3,4,1},
{1,4,8,7,1},
{1,5,14,18,11,1},
{1,6,21,40,36,16,1},
{1,7,30,72,98,66,22,1},
{1,8,40,119,211,214,113,29,1},
{1,9,52,182,398,546,428,183,37,1},...
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PROGRAM
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(PARI) T(n, k)=if(n<k|k<0, 0, if(k==0, 1, sum(j=0, min(k, n-k), binomial(k+j, k-j)*T(n-k, j))))
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CROSSREFS
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Cf. A092423, A092424, A011973.
Sequence in context: A109225 A112564 A089899 this_sequence A096465 A124460 A122084
Adjacent sequences: A092419 A092420 A092421 this_sequence A092423 A092424 A092425
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KEYWORD
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nonn,tabl
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Mar 22 2004
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