A349016
G.f. A(x) satisfies: A(x) = 1 + x * A(-x) / (1 - x) + x * A(x)^2.
Original entry on oeis.org
1, 2, 3, 12, 26, 125, 317, 1642, 4492, 24188, 69174, 381613, 1123923, 6304781, 18962485, 107682542, 329007674, 1885923378, 5833166568, 33685017384, 105214504816, 611241171298, 1924588709710, 11236434464097, 35617302886643, 208815253200975, 665665428686531
Offset: 0
-
nmax = 26; A[] = 0; Do[A[x] = 1 + x A[-x]/(1 - x) + x A[x]^2 + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
a[0] = 1; a[n_] := a[n] = Sum[a[k] ((-1)^k + a[n - k - 1]), {k, 0, n - 1}]; Table[a[n], {n, 0, 26}]
A349014
G.f. A(x) satisfies: A(x) = 1 + x + x^2 * A(x) / (1 - x) + x^2 * A(x)^2.
Original entry on oeis.org
1, 1, 2, 4, 9, 20, 47, 111, 270, 663, 1656, 4174, 10636, 27308, 70651, 183902, 481436, 1266515, 3346793, 8879116, 23642034, 63156917, 169222939, 454660940, 1224650739, 3306338583, 8945780742, 24252558183, 65872671839, 179228552638, 488443704486
Offset: 0
-
nmax = 30; A[] = 0; Do[A[x] = 1 + x + x^2 A[x]/(1 - x) + x^2 A[x]^2 + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
a[0] = a[1] = 1; a[n_] := a[n] = Sum[a[k] (1 + a[n - k - 2]), {k, 0, n - 2}]; Table[a[n], {n, 0, 30}]
A349015
G.f. A(x) satisfies: A(x) = 1 + x * A(x) / (1 - x) - x * A(x)^2.
Original entry on oeis.org
1, 0, 1, 0, 2, -1, 5, -6, 16, -28, 62, -125, 267, -565, 1213, -2618, 5686, -12418, 27248, -60048, 132848, -294930, 656878, -1467257, 3286219, -7378239, 16603459, -37441989, 84599855, -191501531, 434224405, -986161958, 2243009870, -5108859820, 11651743902
Offset: 0
-
nmax = 34; A[] = 0; Do[A[x] = 1 + x A[x]/(1 - x) - x A[x]^2 + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
a[0] = 1; a[n_] := a[n] = Sum[a[k] (1 - a[n - k - 1]), {k, 0, n - 1}]; Table[a[n], {n, 0, 34}]
A376317
a(n) = P(n+1, n+1) where P(n, m) = P(n, m-1) + P(n-1, m + f(m-n)) for n < m with P(n, m) = P(n-1, m) for 0 <= m <= n and P(0, m) = 1 for m >= 0 and where f(n) = [(n mod 4) > 0].
Original entry on oeis.org
1, 2, 6, 23, 100, 466, 2270, 11413, 58776, 308473, 1643922, 8872220, 48393710, 266357916, 1477471248, 8251090171, 46353709956, 261783417427, 1485374891782, 8463626764923, 48408809202918, 277834282516061, 1599585546691518, 9235769089804804, 53466364700486982
Offset: 0
-
upto(n) = my(v1); v1 = vector(2*(n+1), i, 1); v2 = vector(n+1, i, 0); v2[1] = 1; for(i=1, n, for(j=i+1, 2*(n+1)-i, v1[j] = v1[j+(((j-i)%4)>0)] + v1[j-1]); v2[i+1] = v1[i+1]); v2
Showing 1-4 of 4 results.
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