A169634 -id:A169634 - cp's OEIS frontend

A174971 Periodic sequence: Repeat 3, -3.

3, -3, 3, -3, 3, -3, 3, -3, 3, -3, 3, -3, 3, -3, 3, -3, 3, -3, 3, -3, 3, -3, 3, -3, 3, -3, 3, -3, 3, -3, 3, -3, 3, -3, 3, -3, 3, -3, 3, -3, 3, -3, 3, -3, 3, -3, 3, -3, 3, -3, 3, -3, 3, -3, 3, -3, 3, -3, 3, -3, 3, -3, 3, -3, 3, -3, 3, -3, 3, -3, 3, -3, 3, -3, 3, -3, 3, -3, 3, -3, 3, -3, 3, -3

Offset: 0

Klaus Brockhaus, Apr 04 2010

Interleaving of A010701 and -A010701; signed version of A010701.
Essentially first differences of A010674.
Inverse binomial transform of 3 followed by A000004.
Second inverse binomial transform of A010701.
Third inverse binomial transform of A007283.
Fourth inverse binomial transform of A000244 without initial term 1.
Fifth inverse binomial transform of A164346.
Sixth inverse binomial transform of A005053 without initial term 1.
Seventh inverse binomial transform of A169604.
Eighth inverse binomial transform of A169634.
Ninth inverse binomial transform of A103333 without initial term 1.
Tenth inverse binomial transform of A013708.
Eleventh inverse binomial transform of A093138 without initial term 1.

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

Cf. A010701 (all 3's sequence), A000004 (all zeros sequence), A007283 (3*2^n), A000244 (powers of 3), A164346 (3*4^n), A005053 (expand (1-2x)/(1-5x)), A169604 (3*6^n), A169634 (3*7^n), A103333 (expand (1-5x)/(1-8x)), A013708 (3^(2n+1)), A093138 (expand (1-7x)/(1-10x)).

&cat[ [3, -3]: n in [0..41] ];
[ 3*(-1)^n: n in [0..83] ];

PadRight[{},120,{3,-3}] (* or *) NestList[-1#&,3,120] (* Harvey P. Dale, Dec 30 2023 *)

a(n)=3*(-1)^n \\ Charles R Greathouse IV, Jun 13 2013

a(n) = 3*(-1)^n.
a(n) = -a(n-1) for n > 0; a(0) = 3.
a(n) = a(n-2) for n > 1; a(0) = 3, a(1) = -3.
G.f.: 3/(1+x).

A338717 a(n) = sum of 4th powers of entries in row n of Stern's triangle A337277.

Original entry on oeis.org

1, 3, 37, 395, 4277, 46251, 500213, 5409835, 58507765, 632765739, 6843407605, 74011952171, 800444658677, 8656867341099, 93624651434741, 1012557431099947, 10950882439229941, 118434591969329451, 1280878746784164085, 13852797030687146027, 149819009843990278133

Offset: 0

N. J. A. Sloane, Nov 19 2020

Richard P. Stanley, Some Linear Recurrences Motivated by Stern's Diatomic Array, arXiv:1901.04647 [math.CO], 2019. Also American Mathematical Monthly 127.2 (2020): 99-111.
Index entries for linear recurrences with constant coefficients, signature (10,9,-2).

Cf. A337277.

For 2nd and 3rd powers see A052984, A169634.

LinearRecurrence[{10,9,-2},{1,3,37},30] (* Harvey P. Dale, Apr 07 2022 *)

G.f.: -(2*x^2+7*x-1)/((x+1)*(2*x^2-11*x+1)). - Alois P. Heinz, Nov 19 2020

cp's OEIS Frontend

A174971 Periodic sequence: Repeat 3, -3.

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