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A319384 a(n) = a(n-1) + 2*a(n-2) - 2*a(n-3) - a(n-4) + a(n-5), a(0)=1, a(1)=5, a(2)=9, a(3)=21, a(4)=29. 1
1, 5, 9, 21, 29, 49, 61, 89, 105, 141, 161, 205, 229, 281, 309, 369, 401, 469, 505, 581, 621, 705, 749, 841, 889, 989, 1041, 1149, 1205, 1321, 1381, 1505, 1569, 1701, 1769, 1909, 1981, 2129, 2205, 2361 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The two bisections A136392(n+1)=1,9,29,61, ... and A201279(n)=5,21,49, ... are in the hexagonal spiral based on 2*n+1:

.

                    67--65--63--61

                    /             \

                  69  33--31--29  59

                  /   /         \   \

                71  35  11---9  27  57

                /   /   /     \   \   \

              73  37  13   1   7  25  55

                  /   /   /   /   /   /

                39  15   3---5  23  53

                  \   \         /   /

                  41  17--19--21  51

                    \             /

                    43--45--47--49

.

A201279(n) - A136892(n) = 20*n.

LINKS

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

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

FORMULA

a(2*n) = A136392(n+1), a(2*n+1) = A201279(n).

a(-n) = a(n).

a(2*n) + a(2*n+1) = 6*A001844(n).

a(n) = (6*n^2 + 6*n + 5 - (2*n + 1)*(-1)^n)/4. - Wesley Ivan Hurt, Oct 04 2018

G.f.: (1 + x^2)*(1 + 4*x + x^2) / ((1 - x)^3*(1 + x)^2). - Colin Barker, Jun 05 2019

a(n) = A104585(n) + A032766(n+1). - Alex W. Nowak, Jan 08 2021

MATHEMATICA

Table[(6 n^2 + 6 n + 5 - (2 n + 1)*(-1)^n)/4, {n, 0, 80}] (* Wesley Ivan Hurt, Jan 07 2021 *)

PROG

(PARI) Vec((1 + x^2)*(1 + 4*x + x^2) / ((1 - x)^3*(1 + x)^2) + O(x^50)) \\ Colin Barker, Jun 05 2019

(MAGMA) [(6*n^2 + 6*n + 5 - (2*n + 1)*(-1)^n)/4 : n in [0..50]]; // Wesley Ivan Hurt, Jan 19 2021

CROSSREFS

Cf. A001844.

In the spiral: A003154(n+1), A080859, A126587, A136392, A201279, A227776.

Cf. A032766, A104585.

Sequence in context: A273739 A169709 A269523 * A211427 A273410 A273486

Adjacent sequences:  A319381 A319382 A319383 * A319385 A319386 A319387

KEYWORD

nonn,easy

AUTHOR

Paul Curtz, Sep 18 2018

STATUS

approved

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Last modified May 9 11:44 EDT 2021. Contains 343740 sequences. (Running on oeis4.)