A135098 -id:A135098 - cp's OEIS frontend

A136482 Triangle read by rows: T(n,k) = 2*A007318(n,k) - A034851(n,k) (i.e., twice Pascal's triangle - the Losanitch triangle).

1, 1, 1, 1, 3, 1, 1, 4, 4, 1, 1, 6, 8, 6, 1, 1, 7, 14, 14, 7, 1, 1, 9, 21, 30, 21, 9, 1, 1, 10, 30, 51, 51, 30, 10, 1, 1, 12, 40, 84, 102, 84, 40, 12, 1, 1, 13, 52, 124, 186, 186, 124, 52, 13, 1, 1, 15, 65, 180, 310, 378, 310, 180, 65, 15, 1, 1, 16, 80, 245, 490, 688, 688, 490, 245

Offset: 0

Gary W. Adamson, Dec 31 2007

Row sums are apparently in A135098. - R. J. Mathar, May 01 2008

			Row n=3 is 2*(1,3,3,1) - (1,2,2,1) = (1,4,4,1).

Cf. A007318, A034851, A136489.

A007318 := proc(n,k) binomial(n,k) ; end: A051159 := proc(n,k) binomial(n mod 2, k mod 2)*binomial(floor(n/2),floor(k/2)) ; end: A034851 := proc(n,k) (A007318(n,k)+A051159(n,k))/2 ; end: A136482 := proc(n,k) 2*A007318(n,k)-A034851(n,k) ; end: for n from 0 to 13 do for k from 0 to n do printf("%d,",A136482(n,k)) ; od: od: # R. J. Mathar, May 01 2008

Edited and corrected by R. J. Mathar, May 01 2008

A136488 a(n) = 2^n - A005418(n).

Original entry on oeis.org

1, 2, 5, 10, 22, 44, 92, 184, 376, 752, 1520, 3040, 6112, 12224, 24512, 49024, 98176, 196352, 392960, 785920, 1572352, 3144704, 6290432, 12580864, 25163776, 50327552, 100659200, 201318400, 402644992, 805289984, 1610596352, 3221192704, 6442418176, 12884836352

Offset: 1

Gary W. Adamson, Jan 01 2008

			a(5) = 22 = 2^5 - A005418(5) = 32 - 10.
a(5) = 22 = sum of row 5 terms of triangle A136482 = (1 + 6 + 8 + 6 + 1).

Colin Barker, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (2,2,-4).

Cf. A005418, A135098, A136482.

[2^n - (2^(n - 2) + 2^(Floor(n/2) - 1)): n in [1..40]]; // G. C. Greubel, Nov 02 2018

Table[2^n - (2^(n - 2) + 2^(Floor[n/2] - 1)), {n, 40}] (* after Harvey P. Dale at A005418, or *)
CoefficientList[Series[(1 - x^2)/(1 - 2 x - 2 x^2 + 4 x^3), {x, 0, 40}], x] (* Michael De Vlieger, Sep 23 2016 *)

Vec(x*(1-x)*(1+x)/((1-2*x)*(1-2*x^2)) + O(x^40)) \\ Colin Barker, Sep 23 2016

a(n) = 2^n - A005418(n). Sum of (n-1)-th row terms of triangle A136482.
G.f.: x*(1 - x^2)/(1 - 2*x - 2*x^2 + 4*x^3). - Michael De Vlieger, Sep 23 2016
From Colin Barker, Sep 23 2016: (Start)
a(n) = 3*2^(n-2)-2^(n/2-1) for n even.
a(n) = 3*2^(n-2)-2^((n-3)/2) for n odd.
(End)
a(n) = A135098(n-1) for n >= 1. - Georg Fischer, Nov 02 2018

More terms from Colin Barker, Mar 19 2013

Missing a(4) added by Michael De Vlieger, Sep 23 2016

cp's OEIS Frontend

A136482 Triangle read by rows: T(n,k) = 2*A007318(n,k) - A034851(n,k) (i.e., twice Pascal's triangle - the Losanitch triangle).

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A136488 a(n) = 2^n - A005418(n).

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