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Search: id:A102662
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| A102662 |
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Triangle read by rows: T(1,1)=1,T(2,1)=1,T(2,2)=3, T(k-1,r-1)+T(k-1,r)+T(k-2,r-1). |
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+0
1
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| 1, 1, 3, 1, 5, 3, 1, 7, 11, 3, 1, 9, 23, 17, 3, 1, 11, 39, 51, 23, 3, 1, 13, 59, 113, 91, 29, 3, 1, 15, 83, 211, 255, 143, 35, 3, 1, 17, 111, 353, 579, 489, 207, 41, 3, 1, 19, 143, 547, 1143, 1323, 839, 283, 47, 3, 1, 21, 179, 801, 2043, 3045, 2651, 1329, 371, 53, 3, 1, 23, 219
(list; table; graph; listen)
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OFFSET
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1,3
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COMMENT
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Generalization of A008288 (use initial terms 1,1,3). Triangle seen as lower triangular matrix: The absolute values of the coefficients of the characteristic polynomials of the n X n matrix are the (n+1)th row of A038763. Row sums give A048654.
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REFERENCES
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Boris A. Bondarenko, "Generalized Pascal Triangles and Pyramids" Fibonacci Association, 1993, p. 37
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EXAMPLE
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Triangle begins:
1
1 3
1 5 3
1 7 11 3
1 9 23 17 3
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PROGRAM
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(PARI) T(k, r)=if(r>k, 0, if(k==1, 1, if(k==2, if(r==1, 1, 3), if(r==1, 1, if(r==k, 3, T(k-1, r-1)+T(k-1, r)+T(k-2, r-1)))))) BM(n) = M=matrix(n, n); for(i=1, n, for(j=1, n, M[i, j]=T(i, j))); M M=BM(10) for(i=1, 10, s=0; for(j=1, i, s+=M[i, j]); print1(s, ", "))
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CROSSREFS
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Cf. A038763, A048654, A008288.
Sequence in context: A133094 A159291 A122510 this_sequence A142048 A117563 A060439
Adjacent sequences: A102659 A102660 A102661 this_sequence A102663 A102664 A102665
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KEYWORD
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nonn,tabl
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AUTHOR
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Lambert Klasen (lambert.klasen(AT)gmx.net) and Gary W. Adamson (qntmpkt(AT)yahoo.com), Feb 03 2005
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