A191584
Diagonal sums of the Riordan matrix (1/(1-3*x^2),x/(1-x)) (A191582).
Original entry on oeis.org
1, 0, 4, 1, 14, 6, 47, 26, 154, 99, 496, 352, 1577, 1200, 4964, 3977, 15502, 12918, 48103, 41338, 148490, 130779, 456416, 410048, 1397905, 1276512, 4268740, 3950929, 13002638, 12170598, 39522143, 37343834, 119912698, 114209811, 363262672, 348332320, 1099015481, 1059927312
Offset: 0
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Table[3^(Floor[n/2]+1)-Fibonacci[n+3],{n,0,100}]
LinearRecurrence[{1,4,-3,-3},{1,0,4,1},40] (* Harvey P. Dale, Feb 23 2023 *)
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makelist(3^(floor(n/2)+1)-fib(n+3),n,0,12);
A191585
Central coefficients of the Riordan matrix (1/(1-3*x^2),x/(1-x)) (A191582).
Original entry on oeis.org
1, 1, 6, 19, 74, 276, 1056, 4047, 15606, 60382, 234356, 911802, 3554864, 13883650, 54304788, 212687199, 833958918, 3273341382, 12859792932, 50562992490, 198954466524, 783371113152, 3086377703184, 12166795814166, 47987669811276, 189361785529476
Offset: 0
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Table[Sum[Binomial[2n-2i-1,n-2i]3^i,{i,0,n/2}],{n,0,25}]
CoefficientList[Series[(2-11x+12x^2+(2-9x)Sqrt[1-4x])/(2(1-4x)(2- 6x-9x^2)),{x,0,30}],x] (* Harvey P. Dale, Jun 10 2011 *)
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makelist(sum(binomial(2*n-2*i-1,n-2*i)*3^i,i,0,n/2),n,0,25);
A279010
Alternating Jacobsthal triangle A_3(n,k) read by rows.
Original entry on oeis.org
1, 1, 1, 3, 0, 1, 3, 3, -1, 1, 9, 0, 4, -2, 1, 9, 9, -4, 6, -3, 1, 27, 0, 13, -10, 9, -4, 1, 27, 27, -13, 23, -19, 13, -5, 1, 81, 0, 40, -36, 42, -32, 18, -6, 1, 81, 81, -40, 76, -78, 74, -50, 24, -7, 1, 243, 0, 121, -116, 154, -152, 124, -74, 31, -8, 1
Offset: 0
Triangle begins:
1;
1, 1;
3, 0, 1;
3, 3, -1, 1;
9, 0, 4, -2, 1;
9, 9, -4, 6, -3, 1;
27, 0, 13, -10, 9, -4, 1;
27, 27, -13, 23, -19, 13, -5, 1;
81, 0, 40, -36, 42, -32, 18, -6, 1;
81, 81, -40, 76, -78, 74, -50, 24, -7, 1;
243, 0, 121, -116, 154, -152, 124, -74, 31, -8, 1;
...
If initial column is omitted, this is very like the Riordan matrix
A191582.
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A[n_, 0] := 3^Floor[n/2];
A[n_, k_] /; (k<0 || t>n) = 0;
A[n_, n_] = 1;
A[n_, k_] := A[n, k] = A[n-1, k-1] - A[n-1, k];
Table[A[n, k], {n, 0, 10}, {k, 0, n}] // Flatten (* Jean-François Alcover, Aug 12 2018 *)
A235501
Riordan array (1/(1-2*x^2), x/(1-x)).
Original entry on oeis.org
1, 0, 1, 2, 1, 1, 0, 3, 2, 1, 4, 3, 5, 3, 1, 0, 7, 8, 8, 4, 1, 8, 7, 15, 16, 12, 5, 1, 0, 15, 22, 31, 28, 17, 6, 1, 16, 15, 37, 53, 59, 45, 23, 7, 1, 0, 31, 52, 90, 112, 104, 68, 30, 8, 1, 32, 31, 83, 142, 202, 216, 172, 98, 38, 9, 1, 0, 63, 114, 225
Offset: 0
Triangle begins (0<=k<=n):
1
0, 1
2, 1, 1
0, 3, 2, 1
4, 3, 5, 3, 1
0, 7, 8, 8, 4, 1
8, 7, 15, 16, 12, 5, 1
0, 15, 22, 31, 28, 17, 6, 1
Showing 1-4 of 4 results.
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