A053743 Sum of numbers in range 10*n to 10*n+9.

45, 145, 245, 345, 445, 545, 645, 745, 845, 945, 1045, 1145, 1245, 1345, 1445, 1545, 1645, 1745, 1845, 1945, 2045, 2145, 2245, 2345, 2445, 2545, 2645, 2745, 2845, 2945, 3045, 3145, 3245, 3345, 3445, 3545, 3645, 3745, 3845, 3945, 4045, 4145, 4245, 4345

Offset: 0

Author

Odimar Fabeny, Feb 13 2000

Keywords

• nonn
• easy

Examples

			45 = sum of 0, 1, 2, 3, 4, 5, 6, 7, 8, 9;
145 = sum of 10, 11, 12, 13, 14, 15, 16, 17, 18, 19.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..1000
• Tanya Khovanova, Recursive Sequences
• Index entries for linear recurrences with constant coefficients, signature (2,-1).

Crossrefs

Cf. A053741, A053742.

Programs

GAP

List([0..50], n-> 5*(20*n+9)); # G. C. Greubel, Sep 06 2019

Magma

[5*(20*n+9): n in [0..50]]; // G. C. Greubel, Sep 06 2019

Maple

seq(5*(20*n+9), n=0..50); # G. C. Greubel, Sep 06 2019

Mathematica

LinearRecurrence[{2,-1},{45,145},50] (* or *) 100*Range[50]-55 (* Harvey P. Dale, Feb 03 2019 *)

PARI

vector(50, n, 5*(20*n -11)) \\ G. C. Greubel, Sep 06 2019

Sage

[5*(20*n+9) for n in (0..50)] # G. C. Greubel, Sep 06 2019

Formula

a(n) = 100*n + 45.

From Colin Barker, Jun 26 2012: (Start)

a(n) = 2*a(n-1) - a(n-2).

G.f.: 5*(9+11*x)/(1-x)^2. (End)

E.g.f.: 5*(9 + 20*x)*exp(x). - G. C. Greubel, Sep 06 2019

Extensions

More terms from James Sellers, Feb 22 2000