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A176489 Triangle T(n,k) = A176487(n,k)+A176488(n,k)-1 read by rows 0<=k<=n. 1

%I #8 Jun 17 2015 04:00:34

%S 1,1,1,1,12,1,1,35,35,1,1,82,206,82,1,1,177,922,922,177,1,1,368,3599,

%T 7284,3599,368,1,1,751,12917,46923,46923,12917,751,1,1,1518,43876,

%U 264810,468706,264810,43876,1518,1,1,3053,143588,1365740,3931310

%N Triangle T(n,k) = A176487(n,k)+A176488(n,k)-1 read by rows 0<=k<=n.

%C Row sums are 1, 2, 14, 72, 372, 2200, 15220, 121184, 1089116, 10887384, 119752404,....

%C The row sums s(n) seem to obey (-45*n+124)*s(n) +(45*n^2+127*n-654)*s(n-1) +(-206*n^2+227*n+708)*s(n-2) +(303*n^2-869*n+458)*s(n-3) -2*(71*n-125)*(n-2)*s(n-4)=0. - _R. J. Mathar_, Jun 16 2015

%e 1;

%e 1, 1;

%e 1, 12, 1;

%e 1, 35, 35, 1;

%e 1, 82, 206, 82, 1;

%e 1, 177, 922, 922, 177, 1;

%e 1, 368, 3599, 7284, 3599, 368, 1;

%e 1, 751, 12917, 46923, 46923, 12917, 751, 1;

%e 1, 1518, 43876, 264810, 468706, 264810, 43876, 1518, 1;

%e 1, 3053, 143588, 1365740, 3931310, 3931310, 1365740, 143588, 3053, 1;

%e 1, 6124, 457997, 6610700, 29214758, 47173244, 29214758, 6610700, 457997, 6124, 1;

%p A176489 := proc(n,k)

%p A176487(n,k)+A176488(n,k)-1 ;

%p end proc: # _R. J. Mathar_, Jun 16 2015

%t << DiscreteMath`Combinatorica`;

%t t[n_, m_, 0] := Binomial[n, m];

%t t[n_, m_, 1] := Eulerian[1 + n, m];

%t t[n_, m_, q_] := t[n, m, q] = t[n, m, q - 1] + t[n, m, q - 2] - 1;

%t Table[Flatten[Table[Table[t[n, m, q], {m, 0, n}], {n, 0, 10}]], {q, 0, 10}]

%Y Cf. A007318, A008292.

%K nonn,tabl,easy

%O 0,5

%A _Roger L. Bagula_, Apr 19 2010

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Last modified March 28 14:38 EDT 2024. Contains 371254 sequences. (Running on oeis4.)