A164851 -id:A164851 - cp's OEIS frontend

A164855 Generalized Lucas-Pascal triangle: (101*100^n,1).

1, 101, 1, 10100, 102, 1, 1010000, 10202, 103, 1, 101000000, 1020202, 10305, 104, 1, 10100000000, 102020202, 1030507, 10409, 105, 1, 1010000000000, 10202020202, 103050709, 1040916, 10514, 106, 1, 101000000000000, 1020202020202

Offset: 0

Mark Dols, Aug 28 2009

			Triangle begins:
1
101,1
10100,102,1
1010000,10202,103,1
101000000,1020202,10305,104,1
10100000000,102020202,1030507,10409,105,1
1010000000000,10202020202,103050709,1040916,10514,106,1
101000000000000,1020202020202,10305070911,104091625,1051430,10620,107,1

Cf. A164847, A164851, A029635, A228196.

A164855 := proc(n,k)
    option remember;
    if n=k then
        1;
    elif k>n or k<0 then
        0;
    elif k = 0 then
        101*100^(n-1) ;
    else
        procname(n-1,k-1)+procname(n-1,k) ;
    end if;
end proc:
seq(seq(A164855(n,k),k=0..n),n=0..12) ; # R. J. Mathar, Nov 03 2016

T(0,0)=1, T(n+1,0)=101*100^n, T(n,n)=1, T(n,k)=T(n-1,k-1)+T(n-1,k) for 0Philippe Deléham, Dec 27 2013

Initial 1 added by Philippe Deléham, Dec 27 2013

A164852 Diagonal sum of generalized Lucas-Pascal triangle;(11*10^n,1).

Original entry on oeis.org

1, 12, 13, 124, 137, 1251, 1388, 12539, 13927, 125466, 139393, 1254859, 1394252, 12549111, 13943363, 125492474, 139435837, 1254928311, 1394364148, 12549292459, 13943656607, 125492949066, 139436605673, 1254929554739, 1394366160412, 12549295715151

Offset: 1

Mark Dols, Aug 28 2009

Index entries for linear recurrences with constant coefficients, signature (1,11,-10,-10).

A164851, A000032

LinearRecurrence[{1,11,-10,-10},{1,12,13,124},40] (* Harvey P. Dale, Aug 05 2018 *)

G.f.: -x*(-1-11*x+10*x^2+11*x^3) / ( (10*x^2-1)*(x^2+x-1) ). - R. J. Mathar, Nov 03 2016

More terms from Harvey P. Dale, Aug 05 2018

A179619 a(1)=1, a(n+1) = 10a(n)+2n-1.

Original entry on oeis.org

1, 13, 135, 1357, 13579, 135801, 1358023, 13580245, 135802467, 1358024689, 13580246911, 135802469133, 1358024691355, 13580246913577, 135802469135799, 1358024691358021, 13580246913580243, 135802469135802465, 1358024691358024687, 13580246913580246909

Offset: 1

Mark Dols, Jul 20 2010

Third column of A164851. The repeating pattern corresponds to the decimal expansion of 11/81 = 0.13580246913580246...

Colin Barker, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (12,-21,10).

Cf. A164851.

RecurrenceTable[{a[1] == 1, a[n] == 10 a[n - 1] + 2 n - 1}, a, {n,
30}] (* or *) LinearRecurrence[{12,-21,10},{1,13,135},30] (* Harvey P. Dale, Aug 16 2012 *)

Vec(-x*(x+1)/((x-1)^2*(10*x-1)) + O(x^30)) \\ Colin Barker, Oct 03 2015

a(1)=1, a(2)=13, a(3)=135, a(n) = 12*a(n-1)-21*a(n-2)+10*a(n-3). - Harvey P. Dale, Aug 16 2012

G.f.: -x*(x+1) / ((x-1)^2*(10*x-1)). - Colin Barker, Oct 03 2015

cp's OEIS Frontend

A164855 Generalized Lucas-Pascal triangle: (101*100^n,1).

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A164852 Diagonal sum of generalized Lucas-Pascal triangle;(11*10^n,1).

Views

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A179619 a(1)=1, a(n+1) = 10a(n)+2n-1.

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cp's OEIS Frontend

A164855 Generalized Lucas-Pascal triangle: (101*100^n,1).

Views

Author

Keywords

Examples

Crossrefs

Programs

Maple

Formula

Extensions

A164852 Diagonal sum of generalized Lucas-Pascal triangle;(11*10^n,1).

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

Formula

Extensions

A179619 a(1)=1, a(n+1) = 10*a(n)+2*n-1.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

PARI

Formula

A179619 a(1)=1, a(n+1) = 10a(n)+2n-1.