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A155118
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Array T(n,k) ready by antidiagonals: the k-th term of the n-th iterated differences of A140429.
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1
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0, 1, 1, 1, 2, 3, 3, 4, 6, 9, 5, 8, 12, 18, 27, 11, 16, 24, 36, 54, 81, 21, 32, 48, 72, 108, 162, 243, 43, 64, 96, 144, 216, 324, 486, 729, 85, 128, 192, 288, 432, 648, 972, 1458, 2187, 171, 256, 384, 576, 864, 1296, 1944, 2916, 4374, 6561, 341, 512, 768
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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COMMENTS
| Deleting column k=0 and reading by antidiagonals yields A036561. Deleting column k=0 and reading the antidiagonals downwards yields A175840.
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LINKS
| Nathaniel Johnston, Table of n, a(n) for n = 0..10000
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FORMULA
| T(0,k) = A140429(k) = A000244(k-1). T(n,k) = T(n-1,k+1)-T(n-1,k), n>0.
T(n,k) = 2^n*3^(k-1), k>0.
T(n,0) = A001045(n).
T(n,1) = A000079(n).
T(n,2) = A007283(n).
T(n,3) = A005010(n).
T(n,4) = A175806(n).
T(1,k) = A025192(k). T(2,k) = A003946(k).
T(0,k) - T(k+1,0) = 4*A094705(k-2).
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EXAMPLE
| The array starts in row n=0 with columns k>=0 as:
0 1 3 9 27 81 243 729 2187 ...
1 2 6 18 54 162 486 1458 4374 ...
1 4 12 36 108 324 972 2916 8748 ...
3 8 24 72 216 648 1944 5832 17496 ...
5 16 48 144 432 1296 3888 11664 34992 ...
11 32 96 288 864 2592 7776 23328 69984 ...
21 64 192 576 1728 5184 15552 46656 139968 ...
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MAPLE
| T:=proc(n, k)if(k>0)then return 2^n*3^(k-1):else return (2^n - (-1)^n)/3:fi:end:
for d from 0 to 8 do for m from 0 to d do print(T(d-m, m)):od:od: ##Nathaniel Johnston, Apr 13 2011
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CROSSREFS
| Cf. A046936.
Sequence in context: A116494 A036031 A017818 * A091275 A046936 A187067
Adjacent sequences: A155115 A155116 A155117 * A155119 A155120 A155121
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KEYWORD
| nonn,tabl,easy
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AUTHOR
| Paul Curtz (bpcrtz(AT)free.fr), Jan 20 2009
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EXTENSIONS
| a(22) - a(57) from Nathaniel Johnston (nathaniel(AT)nathanieljohnston.com), Apr 13 2011
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