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Search: id:A067763
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| A067763 |
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Square array read by antidiagonals of base n numbers written as 122...222 with k 2's (and a suitable interpretation for n=0, 1 or 2). |
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| 1, 2, 1, 2, 3, 1, 2, 5, 4, 1, 2, 7, 10, 5, 1, 2, 9, 22, 17, 6, 1, 2, 11, 46, 53, 26, 7, 1, 2, 13, 94, 161, 106, 37, 8, 1, 2, 15, 190, 485, 426, 187, 50, 9, 1, 2, 17, 382, 1457, 1706, 937, 302, 65, 10, 1, 2, 19, 766, 4373, 6826, 4687, 1814, 457, 82, 11, 1, 2, 21, 1534, 13121
(list; table; graph; listen)
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OFFSET
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0,2
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COMMENT
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Start with a node; step one is to connect that node to n+1 new nodes so that it is of degree n+1; further steps are to connect each existing node of degree 1 to n new nodes so that it is of degree n+1; T(n,k) is the total number of nodes after k steps.
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FORMULA
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T(n, k) =((n+1)*n^k-2)/(n-1) [with T(1, k)=2k+1] =n*T(n, k-1)+2 =(n+1)*T(n, k-1)-n*T(n, k-2) =T(n, k-1)+(1+1/n)*n^k =A055129(k, n)+A055129(k-1, n). Coefficient of x^k in expansion of (1+x)/((1-x)(1-nx)).
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EXAMPLE
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Rows start: 1,2,2,2,2,2,...; 1,3,5,7,9,11,...; 1,4,10,22,46,94,...; 1,5,17,53,161,485,... T(3,2) =122 base 3 =17.
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CROSSREFS
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Rows include A040000, A005408, A033484, A048473, A020989, A057651, A061801 etc. For negative n (not shown) absolute values of rows would effectively include A000012, A014113, A046717.
Sequence in context: A064882 A065158 A029653 this_sequence A087730 A126247 A101161
Adjacent sequences: A067760 A067761 A067762 this_sequence A067764 A067765 A067766
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KEYWORD
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base,nonn,tabl
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AUTHOR
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Henry Bottomley (se16(AT)btinternet.com), Feb 06 2002
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