A271508 Numbers that are congruent to {1,4} mod 10.

1, 4, 11, 14, 21, 24, 31, 34, 41, 44, 51, 54, 61, 64, 71, 74, 81, 84, 91, 94, 101, 104, 111, 114, 121, 124, 131, 134, 141, 144, 151, 154, 161, 164, 171, 174, 181, 184, 191, 194, 201, 204, 211, 214, 221, 224, 231, 234, 241, 244, 251, 254, 261, 264, 271, 274

Offset

1,2

Comments

Numbers ending in 1 or 4, Union of A017281 and A017317.

a(n+3) gives the sum of 5 consecutive terms of A004442 starting at A004442(n) for n>0. (i.e., a(4) = 14 = 0+3+2+5+4 = Sum_{i=0..4} A004442(n+i)).

Links

Table of n, a(n) for n=1..56.

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

Formula

G.f.: x*(1+3*x+6*x^2)/((-1+x)^2*(1+x)).

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

a(n) = 5*n - 5 - (-1)^n.

a(n) = -n + 2*A047241(n).

a(n+1) = n + 1 + 2*A042948(n).

Shifted bisections: a(2n+2) = A017317(n), a(2n+1) = A017281(n).

E.g.f.: 5*(x-1)*exp(x) - exp(-x). - G. C. Greubel, Apr 08 2016

Sum_{n>=1} (-1)^(n+1)/a(n) = sqrt(1+2/sqrt(5))*Pi/10 + log(phi)/sqrt(5) + log(2)/5, where phi is the golden ratio (A001622). - Amiram Eldar, Apr 15 2023

Maple

A271508:=n->5*n-5-(-1)^n: seq(A271508(n), n=1..100);

Mathematica

Table[5 n - 5 - (-1)^n, {n, 60}] (* or *)
Select[Range[0, 300], MemberQ[{1, 4}, Mod[#, 10]] &]

Prog

(Magma) [5*n-5-(-1)^n : n in [1..100]];
(PARI) my(x='x+O('x^99)); Vec(x*(1+3*x+6*x^2)/((-1+x)^2*(1+x))) \\ Altug Alkan, Apr 09 2016

Crossrefs

Cf. A001622, A004442, A017281, A017317, A042948, A047241.

Sequence in context: A247521 A285979 A299975 * A284323 A352403 A091436

Adjacent sequences: A271505 A271506 A271507 * A271509 A271510 A271511

Keyword

nonn,easy

Author

Wesley Ivan Hurt, Apr 08 2016

Status

approved