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A176644
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A q-form method for the symmetrical triangle sequence was found based on A000567 Octagonal numbers: q=4;c(n,q)=Product[(q*(3*q - 2))^i, {i, 1, n}];t(n,m,q)=c(n,q)/(c(m,q)*c(n-m,q)- c(n,q)/(c(0,q)*c(n-0,q)+1
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0
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1, 1, 1, 1, 40, 1, 1, 1600, 1600, 1, 1, 64000, 2560000, 64000, 1, 1, 2560000, 4096000000, 4096000000, 2560000, 1, 1, 102400000, 6553600000000, 262144000000000, 6553600000000, 102400000, 1, 1, 4096000000
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OFFSET
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0,5
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COMMENTS
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Row sums are:
{1, 2, 42, 3202, 2688002, 8197120002, 275251404800002, 33575403528192000002,
45097190162432327680000002, 220039764562359091213107200000002,
11821957817940660107345920524288000000002,...}.
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LINKS
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Table of n, a(n) for n=0..29.
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FORMULA
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q=4;
c(n,q)=Product[(q*(3*q - 2))^i, {i, 1, n}];
t(n,m,q)=c(n,q)/(c(m,q)*c(n-m,q)- c(n,q)/(c(0,q)*c(n-0,q)+1
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EXAMPLE
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{1},
{1, 1},
{1, 40, 1},
{1, 1600, 1600, 1},
{1, 64000, 2560000, 64000, 1},
{1, 2560000, 4096000000, 4096000000, 2560000, 1},
{1, 102400000, 6553600000000, 262144000000000, 6553600000000, 102400000, 1},
{1, 4096000000, 10485760000000000, 16777216000000000000, 16777216000000000000, 10485760000000000, 4096000000, 1},
{1, 163840000000, 16777216000000000000, 1073741824000000000000000, 42949672960000000000000000, 1073741824000000000000000, 16777216000000000000, 163840000000, 1},
{1, 6553600000000, 26843545600000000000000, 68719476736000000000000000000, 109951162777600000000000000000000, 109951162777600000000000000000000, 68719476736000000000000000000, 26843545600000000000000, 6553600000000, 1},
{1, 262144000000000, 42949672960000000000000000, 4398046511104000000000000000000000, 281474976710656000000000000000000000000, 11258999068426240000000000000000000000000, 281474976710656000000000000000000000000, 4398046511104000000000000000000000, 42949672960000000000000000, 262144000000000, 1}
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MATHEMATICA
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Clear[t, n, m, c, q];
c[n_, q_] = Product[(q*(3*q - 2))^i, {i, 1, n}];
t[n_, m_, q_] = c[n, q]/(c[m, q]*c[n - m, q]) - c[n, q]/(c[0, q]*c[n - 0, q]) + 1;
Table[Flatten[Table[Table[t[n, m, q], {m, 0, n}], {n, 0, 10}]], {q, 2, 12}]
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CROSSREFS
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Cf. A000567
Sequence in context: A013419 A013420 A156917 * A078084 A037937 A126652
Adjacent sequences: A176641 A176642 A176643 * A176645 A176646 A176647
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KEYWORD
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nonn,tabl,uned
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AUTHOR
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Roger L. Bagula, Apr 22 2010
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STATUS
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approved
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