A063394 -id:A063394 - cp's OEIS frontend

A063396 T(3,n) with T(n,m) as in A063394.

1, 15, 47, 131, 343, 863, 2111, 5055, 11903, 27647, 63487, 144383, 325631, 729087, 1622015, 3588095, 7897087, 17301503, 37748735, 82051071, 177733631, 383778815, 826277887, 1774190591, 3800039423, 8120172543, 17314086911, 36842766335, 78248935423

Offset: 0

Floor van Lamoen, Jul 16 2001

Colin Barker, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (7,-18,20,-8)

Cf. A063394, A063397, A063398.

Join[{1},LinearRecurrence[{7,-18,20,-8},{15,47,131,343},30]] (* Harvey P. Dale, Jul 31 2014 *)

Vec(-(20*x^4-52*x^3+40*x^2-8*x-1)/((x-1)*(2*x-1)^3) + O(x^100)) \\ Colin Barker, May 27 2015

For n>0, 1/4 * [(n+1)(n+2)2^n + 10(n+1)2^n + 6*2^n - 4]. - Ralf Stephan, May 08 2004

G.f.: -(20*x^4-52*x^3+40*x^2-8*x-1) / ((x-1)*(2*x-1)^3). - Colin Barker, May 27 2015

A063397 T(4,n) with T(n,m) as in A063394.

Original entry on oeis.org

1, 31, 111, 343, 979, 2655, 6943, 17663, 43967, 107519, 259071, 616447, 1451007, 3383295, 7823359, 17956863, 40943615, 92798975, 209190911, 469237759, 1047789567, 2329935871, 5161091071, 11391729663, 25060966399, 54962159615, 120191975423, 262127222783

Offset: 0

Floor van Lamoen, Jul 16 2001

Colin Barker, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (9,-32,56,-48,16).

Cf. A063394, A063396, A063398.

LinearRecurrence[{9,-32,56,-48,16},{1,31,111,343,979,2655},30] (* Harvey P. Dale, Mar 30 2024 *)

Vec(-(76*x^5-244*x^4+280*x^3-136*x^2+22*x+1) / ((x-1)*(2*x-1)^4) + O(x^100)) \\ Colin Barker, May 27 2015

a(n) = (6*(-4+27*2^n)+191*2^n*n+15*2^(1+n)*n^2+2^n*n^3)/24 for n>0. - Colin Barker, May 27 2015

G.f.: -(76*x^5-244*x^4+280*x^3-136*x^2+22*x+1) / ((x-1)*(2*x-1)^4). - Colin Barker, May 27 2015

A063398 T(5,n) with T(n,m) as in A063394.

Original entry on oeis.org

1, 63, 255, 863, 2655, 7683, 21287, 57071, 149087, 381311, 958207, 2372095, 5796863, 14007295, 33511423, 79466495, 186949631, 436666367, 1013317631, 2337538047, 5362941951, 12242386943, 27817148415, 62934482943, 141815709695, 318372839423, 712243150847

Offset: 0

Floor van Lamoen, Jul 16 2001

Colin Barker, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (11,-50,120,-160,112,-32).

Cf. A063394, A063396, A063397.

Vec(-(260*x^6-996*x^5+1488*x^4-1088*x^3+388*x^2-52*x-1) / ((x-1)*(2*x-1)^5) + O(x^100)) \\ Colin Barker, May 27 2015

a(n) = (24*(-8+81*2^n)+1671*2^(1+n)*n+803*2^n*n^2+27*2^(1+n)*n^3+2^n*n^4) / 192 for n>0. - Colin Barker, May 27 2015

G.f.: -(260*x^6-996*x^5+1488*x^4-1088*x^3+388*x^2-52*x-1) / ((x-1)*(2*x-1)^5). - Colin Barker, May 27 2015

A063395 T(2n,n) with T(n,m) as in A063394.

Original entry on oeis.org

1, 3, 19, 131, 979, 7683, 62099, 511619, 4271699, 36018179, 305998099, 2615234691, 22459983059, 193665818115, 1675580699539, 14538892408451, 126467748738899, 1102484411211779, 9629327766561299, 84247346901823619, 738200425192338899, 6477139329614712323

Offset: 0

Floor van Lamoen, Jul 16 2001

nonn

Equals 4*A084771(n-1) - 1, n>0.

m=matrix(50,50):for(i=1,50,m[1,i]=1:m[i,1]=1):for(i=2,50, for(k=1,i,x=i-k+1: if(m[x,k]==0,m[x,k]=sum(n=2,k-1,m[x,n])+sum(n=2,x-1,m[n,k])+k+x-1))):for(n=1,24,print1(m[n,n]",")) /* Ralf Stephan */

G.f.: 4x/sqrt(1-10x+9x^2) + (1-2x)/(1-x). - Ralf Stephan, Mar 23 2004

Conjecture: (-n+1)*a(n) +(11*n-17)*a(n-1) +(-19*n+43)*a(n-2) +9*(n-3)*a(n-3)=0. - R. J. Mathar, Jun 10 2013

More terms from Ralf Stephan, Mar 23 2004

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A063396 T(3,n) with T(n,m) as in A063394.

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A063397 T(4,n) with T(n,m) as in A063394.

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A063398 T(5,n) with T(n,m) as in A063394.

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A063395 T(2n,n) with T(n,m) as in A063394.

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