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 A176644 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 0
 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 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS Row sums are: {1, 2, 42, 3202, 2688002, 8197120002, 275251404800002, 33575403528192000002, 45097190162432327680000002, 220039764562359091213107200000002, 11821957817940660107345920524288000000002,...}. LINKS FORMULA 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 EXAMPLE {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} MATHEMATICA 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}] CROSSREFS Cf. A000567 Sequence in context: A013419 A013420 A156917 * A329337 A078084 A037937 Adjacent sequences:  A176641 A176642 A176643 * A176645 A176646 A176647 KEYWORD nonn,tabl,uned AUTHOR Roger L. Bagula, Apr 22 2010 STATUS approved

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Last modified May 15 21:56 EDT 2021. Contains 343930 sequences. (Running on oeis4.)