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A026384 a(n) = Sum_{j=0..i, i=0..n} T(i,j),  where T is the array in A026374. 1
1, 3, 8, 18, 43, 93, 218, 468, 1093, 2343, 5468, 11718, 27343, 58593, 136718, 292968, 683593, 1464843, 3417968, 7324218, 17089843, 36621093, 85449218, 183105468, 427246093, 915527343, 2136230468, 4577636718, 10681152343, 22888183593, 53405761718 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Partial sums of A026383. Number of lattice paths from (0,0) that do not go to right of the line x=n, using the steps U=(1,1), D=(1,-1) and, at levels ...,-4,-2,0,2,4,..., also H=(2,0). Example: a(2)=8 because we have the empty path, U, D, UU, UD, DD, DU and H. - Emeric Deutsch, Feb 18 2004

LINKS

Colin Barker, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (1,5,-5).

FORMULA

G.f.: (1+2*x) / ((1-x)*(1-5*x^2)). - Ralf Stephan, Apr 30 2004

From Colin Barker, Nov 25 2016: (Start)

a(n) = (7*5^(n/2) - 3)/4 for n even.

a(n) = 3*(5^((n+1)/2) - 1)/4 for n odd.

a(n) = a(n-1) + 5*a(n-2) - 5*a(n-3) for n>2.

(End)

MAPLE

a[0]:=0:a[1]:=1:for n from 2 to 100 do a[n]:=5*a[n-2]+3 od: seq(a[n], n=1..29); # Zerinvary Lajos, Mar 17 2008

MATHEMATICA

CoefficientList[Series[(1 + 2 x) / ((1 - x) (1 - 5 x^2)), {x, 0, 33}], x] (* Vincenzo Librandi, Aug 09 2017 *)

PROG

(PARI) Vec((2*x + 1)/(5*x^3 - 5*x^2 - x + 1) + O(x^40)) \\ Colin Barker, Nov 25 2016

(MAGMA) I:=[1, 3, 8]; [n le 3 select I[n] else Self(n-1)+5*Self(n-2)-5*Self(n-3): n in [1..35]]; // Vincenzo Librandi, Aug 09 2017

CROSSREFS

Cf. A026383.

Sequence in context: A191524 A026756 A216631 * A322496 A066143 A110045

Adjacent sequences:  A026381 A026382 A026383 * A026385 A026386 A026387

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling

STATUS

approved

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Last modified September 18 22:48 EDT 2020. Contains 337174 sequences. (Running on oeis4.)