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Search: id:A114163
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| A114163 |
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Triangle read by rows, based on a simple Jacobsthal number recursion rule. |
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+0
1
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| 1, 1, 1, 1, 2, 1, 1, 3, 5, 1, 1, 4, 18, 10, 1, 1, 5, 58, 68, 21, 1, 1, 6, 179, 398, 299, 42, 1, 1, 7, 543, 2169, 3687, 1181, 85, 1, 1, 8, 1636, 11388, 42726, 28488, 4836, 170, 1, 1, 9, 4916, 58576, 481374, 640974, 236436, 19286, 341, 1, 1, 10, 14757, 297796, 5353690
(list; table; graph; listen)
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OFFSET
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0,5
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COMMENT
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Subdiagonal S(n+1,n) is A000975(n+1). Row sums of inverse are 0^n.
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FORMULA
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Number triangle T(n, k)=T(n-1, k-1)+J(k+1)*T(n-1, k) where J(n)=A001045(n); Column k has g.f. x^k/Product(1-J(i+1)x, i, 0, k).
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EXAMPLE
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Triangle begins
1....1....3....5...11...21...43....J(k+1)
1
1....1
1....2....1
1....3....5....1
1....4...18...10....1
1....5...58...68...21....1
1....6..179..398..299...42....1
For example, T(6,3)=398=58+5*68=T(5,2)+J(4)*T(5,3).
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CROSSREFS
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Cf. A111669.
Sequence in context: A128198 A123349 A123352 this_sequence A090234 A007754 A144866
Adjacent sequences: A114160 A114161 A114162 this_sequence A114164 A114165 A114166
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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), Nov 14 2005
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