A113439 a(n) = a(n-1) + Sum_{k=1..floor(n/4)} a(n-4k), with a(0)=1.

1, 1, 1, 1, 2, 3, 4, 5, 8, 12, 17, 23, 34, 50, 72, 101, 146, 212, 306, 436, 627, 905, 1305, 1871, 2689, 3872, 5577, 8014, 11521, 16576, 23858, 34309, 49337, 70968, 102108, 146868, 211233, 303832, 437080, 628708, 904306, 1300737, 1871065, 2691401

Offset

0,5

Comments

If presented in four rows a(4k), a(4k+1), a(4k+2) and a(4k+3), each term is the sum of the previous term in the sequence and the partial sum of its row; see Example section.

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (1,0,0,2,-1).

Formula

a(n) = a(n-1) + 2*a(n-4) - a(n-5).

a(n) = 9*a(n-4) - 28*a(n-8) + 38*a(n-12) - 20*a(n-16) +a(n-20).

G.f.: (1-x^4)/(1-x-2*x^4+x^5).

Example

From Jon E. Schoenfield, Mar 11 2017: (Start)
Table of values T(j,k) = a(4k+j) in 4 rows:
.
  j | k=0     1     2     3     4     5     6     7
----+--------------------------------------------------
  0 |   1     2     8    34   146   627  2689 11521 ...
  1 |   1     3    12    50   212   905  3872 16576 ...
  2 |   1     4    17    72   306  1305  5577 23858 ...
  3 |   1     5    23   101   436  1871  8014 34309 ...
.
    T(2,4) = T(1,4) + T(2,0) + T(2,1) + T(2,2) + T(2,3)
      306  =   212  +    1   +    4   +   17   +   72
(End)

Mathematica

CoefficientList[Series[(1 - x^4)/(1 - x - 2*x^4 + x^5), {x, 0, 50}], x] (* G. C. Greubel, Mar 11 2017 *)
LinearRecurrence[{1, 0, 0, 2, -1}, {1, 1, 1, 1, 2}, 50] (* Harvey P. Dale, Nov 10 2019 *)

Prog

(PARI) x='x+O('x^50); Vec((1-x^4)/(1-x-2*x^4+x^5)) \\ G. C. Greubel, Mar 11 2017

Crossrefs

Cf. A028495, A113435, A113444.

Sequence in context: A225132 A240216 A017821 * A274112 A222105 A018059

Adjacent sequences: A113436 A113437 A113438 * A113440 A113441 A113442

Keyword

nonn,easy

Author

Floor van Lamoen, Nov 04 2005

Status

approved